It's not unstable; as you noted yourself, it has some residual mains breakthrough.

Based on the pulse shape it looks like it comes from the narrow, high current cap charging pulses. These occur when the secondary voltage in its cycle climbs above the cap voltage and the diodes start to conduct to top up the caps.

These current pulses can be quite high, especially if you use a lot of capacitance after the rectifier. Even a fractional ohm resistance in the ground or return line can cause some mV across them. A simple test could be to remove all load from the psu, that should also make those pulses disappear or greatly diminish.

Then again, you may be just having your scope probe ground lead at a bad point - try to measure directly at the supply output or directly across the capacitor.

Just adding to what Jan mentioned... try connecting your scope probe tip and its ground lead together. You should get a noise free trace of course. Now keeping them shorted connect the two to the same ground point you used before. If the trace now shows a problem, then that suggests a grounding issue via the scope.

Missed the oscillations bit. Most regulated supplies (with feedback) are unstable without an output cap. Data sheets will give min required cap - read them!
Most are OK with anything above a few uF. And don't use film or other boutique caps there, you need the ESR for stability.

It's not unstable; as you noted yourself, it has some residual mains breakthrough.

Based on the pulse shape it looks like it comes from the narrow, high current cap charging pulses. These occur when the secondary voltage in its cycle climbs above the cap voltage and the diodes start to conduct to top up the caps.

These current pulses can be quite high, especially if you use a lot of capacitance after the rectifier. Even a fractional ohm resistance in the ground or return line can cause some mV across them. A simple test could be to remove all load from the psu, that should also make those pulses disappear or greatly diminish.

Then again, you may be just having your scope probe ground lead at a bad point - try to measure directly at the supply output or directly across the capacitor.

jan

Yes there are no pulses with no load, and increase in amplitude with load.